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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 382, page id 1815201908:0439
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.86
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B abid.
A R A B: OL. A
Demonstratio.
criplicaram esse rarionis A et ul IL O. et hc de cereris. Ouo d tuic demonstrandum.
TE ABC parabolae diameter BD, divila in F. R F, vE BF, BD, BF
Voniam AE, AF, AC, AD, ecC. sune continux proporciotales d corius seriet
38. huius exie ratio AMI ad A P, criplicaca eruS. Chius duplicacam HaBCEMIF 2d PI: est 2V
Ponicur AD; erunc quoque AF, AB, AI concinux proportionales, ni-
LmC
mirum secunda, quarra, de sexta. unde cum A D media aequalis ponacurlaterirecto,
cemracio AIF ad P I. duplicata racionis MIE ad BD, cum MF. BD, PI AncPTO
porcionales; igicurratio AM ad A P, criplicara cArarionis MF ad BD, id cA lerru-
plicara eius quam haber NYG ad BD, quia MF, NC, BD Cuncconcinux. eodem
modocum AC, A D, AH sine proporcionales, ostendicurracionem AN ad AO
eriplicacam essc eius cuius duplicaram haber NC ad OFI, id est criplicaram eius
quam habec NC ad BD. undecum AM ad AP. octensa uc rarionem habere (ex-
cuplicacam iphus NVC ad BD, pacee racioriem AM ad AP, duplicacam eAe ra
tionis AN ad AO. eadem prorsus mechodo octendicur; racionem AI. ad AC
PROPOSITIO XLI.
per F _ F ordinaci Ca LII. IIR:
lincproportionales, _ BD media x qualis lareri recto, ponancurque
Dico iunctas AB, HIB ipa LB MePloPOOaIC.
Demonstratio.
Voniam BF, BD, BF cC
tim
une proportionales, de BDme-
dia aequalis lacerirecto, taco P AB ad
EB eriplicaca est eius, cuius duplica.
cam haber AF ad FIF: Ced eadem de
causa quoquerario B C ad B K, cripli
caca eA eius cuius duplicacam habet
C ad FR, id CA A P, ad EI Frigicurr
AB ad HB, AC, C B ad XB: quod
tnc demonteandum.
e e  u u u    e e e  e e es e a  sit e  e t  ut  e  ie u e es   t        l .    .  1 1  . le  et  1e   e t s. u t